
Network radiality is essential for distribution system operations. Some approaches proposed for enforcing radiality are cycle elimination [1]} and virtual commodity flow [2]}, [3]}. The ODNP task needs to identify \(\mathcal {G}^{\prime }=(\mathcal {V},\mathcal {E}^{\prime })\) , a spanning subgraph of \(\mathcal {G}\) , such that every connected component, or simply component, of \(\mathcal {G}^{\prime }\)  is a tree, i.e. \(\mathcal {G}^{\prime }\)  is a forest. A spanning forest may include isolated nodes, i.e. it may have components with a single node. The radiality constraints in this context will be formulated using the condition stated next.
<FIGURE>